For an individual security calculating it's Sharpe and Sortino ratios is straightforward.
What I'm curious about is the following:
Let's say I have a portfolio of several securities, which is a distribution of my total capital: for example Asset A has 25%, Asset B has 50%, and Asset C has 25%. At every timestep t
, let's assume that I can adjust these percentages to maximize my profits, and that the total distribution always has to add up to 100%.
So at each timestep t
my portfolio has a return of r_t
, which is the dot product of the distribution vector (a
) for each asset at time t
with the vector of the change in price for each asset since time t-1
.
If I want to calculate the Sharpe and Sortino for the portfolio, would I:
- Calculate the Sharpe and Sortino ratios for each individual security at time
t
and again take a dot product between my distribution vectora
and the vector of each sharpe/sortino ratio for each security - Directly calculate the Sharpe and Sortino ratios of the portfolio using the returns of the portfolio (
r_t
) across all timestepst
.
Another good question would be: are both of these approaches fundamentally the same?
Thanks in advance for your help!